In recent years, fuzzy regression has emerged as a powerful tool for modeling relationships between independent and dependent variables under uncertainty. In classical linear regression, significant variations in data can reduce the accuracy and reliability of results. Therefore, optimal design for fuzzy regression models is of great importance. In this regard, this study examines and develops the D-optimal method for fuzzy regression models to improve the accuracy, efficiency, and parameter estimation. The fuzzy regression scheme is chosen from optimal design points. The proposed method is examined in the context of models with three classical techniques, and the results show that the suggested approach can expand the applications of fuzzy regression models under complex conditions with data containing significant uncertainty.

  Clustering longitudinal data is a complex task that requires taking into account the similarity of individual trajectories despite scattered and irregular observed times. Clustering is a widely used statistical technique in various fields, such as unsupervised machine learning, data mining, pattern recognition, image analysis, and bioinformatics. This thesis reviews and studies several multivariate longitudinal data clustering algorithms as well as introduces a new clustering algorithm called ClusterMLD. This new method shows promise in identifying meaningful patterns in high-dimensional longitudinal data. The algorithms have been compared using simulation studies and real data to evaluate their performance.

   In this research, heavy metal removal from wastewater was investigated using a combination of electro-Fenton and membrane filtration methods.The integration of these methods was done with the aim of increasing the purification efficiency, and the effect of operating parameters, reaction time, current density, solution acidity (pH), volume ratio of hydrogen peroxide to wastewater, molar ratio of hydrogen peroxide to ferrous ion (Fe2+), nanoparticle concentration and concentration of the input feed was evaluated on the removal percentage of this pollutant. In order to optimize the operating parameters with the aim of maximizing the removal percentage of this pollutant, two optimization methods, the D-optimal criterion which is a real valued function of the value according to Fisher's information matrix and the combined method of artificial neural network-genetic algorithm have been used. The aim of   comparison of statistical analysis for these methods is finding an objective function with the lowest mean squared error.

Abstract In many challenges related to Bayesian inference, we face with some models that have certain complexities and it is necessary to calculate the likelihood function, which is difficult or impossible to calculate. This complexity makes it impossible to get the posterior distribution which is the basis of Bayesian inferences; so, as a solution, simulation methods can be used to estimate the model. One of the methods used in this field is the Approximate Bayesian Computation via >Key­words: Approximate­BayesianComputation, Kullback- Leibler (K-L) divergence, Bayesian inference,likelihood function, summary statistics,      

   Diabetes is a   endocrine disorder characterized by chronic hyperglycemia as a result of insulin resistance or deficiency. Diabetes is one of the most common matebolic diseases in the world and one the challenging problems of the present centary, which is the result of interactions between genetic and behavioral predisposition and environmental factors. Considering the prevalence of type 2 diabetes around the world, it is useful for doctors to identify connections and discore new rules, and for this reason, doctors and researchers analyzed and investigated the cause of the growing increase of this disease by using artificial intelligence and its subset. In this thesis, by using machine learning, including decision tree, random forest, logistic regression and neural network, we analyze and investigate the diagnosis and prognosis of type 2 diabetes by using the data if Ravansar cohort, which includes 10047 people and 137 variables, we understand that the main factors affecting this disease are age, fasting blood sugar level, manganese, selenium, etc. Also, people who are involved with this disease   should change their lifestyle according to the doctor's advice so that they don't face more problems in the rest of their lives. Keywords: Type 2 diabetes, Artificial Intelligenece, Machine Learning, Decision Tree, Random Forest, Logistic Regression, Neural Network.

Unemployment is one of the most important issues in all countries around the world. An increase in the number of unemployed in any society will cause a lot of problems. So having deep and appropriate knowledge of the factors affecting unemployment is taken into account to reduce it. In this thesis, we gathered data of Population and Housing census 2016 from the Statistical Center of Iran. These data categorized the active and unemployed population of 15 years old or above, based on gender and different levels of education in the counties of Iran. We edit these data, based on our purpose. Our purpose in the thesis is spatial modeling of the number of unemployed based on gender and education as covariates. To achieve this goal, we use Bayesian approach and a method called “integrated nested Laplace approximation” or INLA for short. For many years, Bayesian inference has relied upon Markov chain Monte Carlo (MCMC) methods. This approach focuses on estimating the joint posterior distribution of model parameters, therefore, it is computationally expensive in high-dimensional spaces. Instead, Inla focuses on estimating marginal posterior distributions, and according to tremendous developments in computational systems in recent years, it is done more quickly. In addition, INLA is expressed in models with GMRF feature and it has some advantages that reduce the time of model fitting calculations. Finally and after appropriate modeling of the data, we interpret the effects of the two variables of gender and education as well as spatial effects of the counties of Iran on the number of unemployed.

  Regression in Statistics means returning to an average or a verage value, Statisticians have always examined the relation ship between Variables, One of the most common models that fit data, Are regression models. Regression analysis is a Statistical method for analyzing and modeling multivariate data. Aspecial type of regression model is the high dimensional regression model in Which the Volume of Variables independent of the sample size is greater, that is, when is p > n, in these models, because the matrix X is not, complete column rank, therefore estimating the least squares ?ˆOLS is not obtained uniquely and estimating the parameters will not be a good predictor. for this reason, in recent years, methods called penalty regression or contraction methods have been used. such as ridge, lasso, group lasso and elastic net, that in this thesis, the lasso convex function is used. lasso is defind as the L1 norm of the parameters, that ? is the vector of regression coefficients and ? is the penalizing parameter. larger value of ? exerts higher penalty on regression coefficients, resulting in the inclusion of fewer variables in the model. and conversely commonly, a sequence of ? value are generated, and then variables are detected for each value of the series. Thereafter, a value of ? is chosen by k-fold cross-validation, and corresponding set of predictors are included in the model. also for simulation results in this Thesis, InfTh and BIC have been used, and we discuss all these issues in R software. Keywords Weibull regression, Penalty methods, Shrinkage methods, Lasso, Criteria of information theory, Bayesian information criteria

Optimal designs have an important role in many applied areas such as medical, engineering, pharmaceutical and marketing studies. Using such as categories of designs designs can considerably reduce the cost of experiment. Finding an optimal design requires pre-specifying a criterion which needs to be optimized. For samples, these criteriaare chosen as functions of Fisher information matrix. The most popular criterion is D-optimal criterion which is determinant of Fisher information matrix. In a nonlinear model, dependency of this matrix onunknown parameters in an optimal design problem. A number of approaches such as Bayesian, Locally and Minimax optimal designs are suggested in order to solve dependency on the parameters.\\\\In this thesis we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. In order to calculate these designs the Monte Carlo method is used and a general methodology is proposed that allows to find D-optimal designs for any type of non-linear model in the presence of correlated observations, later the designs found are compared by calculating the efficiencies taking as a reference design the one obtained with the a priori Uniform distribution, evidencing that depending on the selected correlation structure there is an a priori effect and finally through the information criteria AIC and BIC the best correlation structure is selected among the structures chosen for then make a simulation study with the purpose of checking and verifying from the point of view of the proposed statisticians.

در مسائل دسته‌بندي، داده‌ها با توجه به وجه اشتراكي كه دارند به چند دسته خاص تقسيم مي‌شوند. دسته‌بندي ابزار مهمي براي تحليل مشكلات آماري است. روش‌هاي متعددي براي دسته‌بندي داده‌ها وجود دارد كه برحسب اينكه متغير پاسخ مشخص و يا نامشخص باشند به ترتيب به دو دسته كلي بانظارت و بدون نظارت تقسيم‌بندي مي‌شوند. از جمله اين روش‌ها مي‌توان به روش‌هاي كلاسيك رگرسيوني مثل رگرسيون با داده‌هاي دودويي (لجستيك، پروبيت و...) اشاره كرد. همچنين روش‌هاي دسته‌بندي براساس آموزش ماشين مثل درخت تصميم، جنگل تصادفي و ... جايگزين‌هاي مناسبي براي روش‌هاي رگرسيون كلاسيك هستند. در اين تحقيق ما به بررسي اين روش‌ها مي‌پردازيم و در نهايت اين روش‌ها، براي مجموعه داده‌هاي بانكي از يك كمپين بازاريابي تلفني به كار برده مي‌شود. روش‌هاي مختلف با استفاده از معيار دقت و منحني ROC مقايسه مي‌گردند.  

  reast cancer is one of the most common cancers in women today. Although men also get this cancer, the risk is more serious in women. Sometimes a misdiagnosis of cancer can lead to the death of a human being, and this should be considered a serious risk. Breast cancer tumors have two types, malignant and benign. Identifying the right type of these tumors will prevent unnecessary treatments and reduce mortality.The aim of this dissertation is to compare five methods of classification, naive Bayes, support vector machine, artificial neural network, logistic regression and random forest on breast cancer data to diagnose benign and malignant cancer tumors to determine the best method according to evaluation criteria. Choose binary, accuracy, precision, sensitivity, specificity, F1 score and Matthews correlation coefficient. The main criterion is to compare the accuracy of the model, then other criteria will be considered.

  The subject of classification is the one of the important issues indifferent sciences. The logistic regression is the one of the statistical methods to classify data in which the underlying distribution of the data is assumed to be known. Today, researchers in addition to statistical methods use other methods such as machine learning to classify data.  In this thesis, the decision trees C4.5, C5, CART, CHAID, and QUEST  are introduced,  and each of them is completely studied. Some ensemble learning algorithms such as random forest, Bagging, and Boosting in the field of supervised learning are also explained. Finally,  using five data sets, we compare the performance of these algorithms with respect to the accuracy measure.

  In this thesis, we develop simple, yet efficient, procedures for sampling approximations of the two-Parameter Poisson-Dirichlet Process and the normalized inverse- Gaussian process. We compare the efficiency of the new approximations to the corresponding stick-breaking approximations of the two-parameter Poisson-Dirichlet Process and the normalized inverse-Gaussian process, in which we demonstrate a substantial improvement.

Estimation of the survival function by using the copula for the inverse Rayleigh distribution.

گاهي اوقات ممكن است نمونه اي كه مشاهده مي كنيم نمونه اي اريب از جامعه باشد. به اين معنا كه تمام اعضا از شانس برابري براي انتخاب شدن در نمونه برخوردار نيستند. براي حل اين مشكل از نسخه اريب-طول كه نسخه ي وزني شده از متغير تصادفي اصلي جامعه است، استفاده مي شود. در نمونه گيري اريب-طول شانس حذف شدن هر واحد از نمونه نااريب، متناسب با طول عمر آن واحد مي باشد. حال آن كه در برخي حالات ممكن است شانس حذف شدن متناسب با طول عمر واحد تحت مطالعه نباشد، از اين رو براي حل اين مشكل مي توان از توزيع هاي وزني استفاده كرد. در اين پايان نامه توزيع اصلي جامعه را گسسته در نظر گرفتيم و سپس با استفاده از تابع ميانگين مانده عمر، توزيع پواسون بريده شده وزني شده و توزيع پواسون آماسيده در صفر بريده شده وزني شده را معرفي كرديم و ويژگي هاي آن ها را مورد بررسي قرار داديم، همچنين نشان داديم مشاهداتي كه ميانگين مانده عمر بزرگ تري دارند شانس بيشتري براي انتخاب شدن در نمونه را دارند. توزيع هاي وزني شده داراي كاربردهاي فراواني در مبحث تحليل بقا و قابليت اعتماد مي باشند، به همين دليل علاوه بر روش شبيه سازي، برخي موارد كاربرد آن با استفاده از داده هاي واقعي نيز تشريح شده است. 

  Today, Copula’s use of the statistical functions which has increased dramatically. Although Copula functions have good advantages in statistical inferences, but when more than bivariate face, there are many computational problems. Therefore, using graphicmodels, wecananalysisthestructureofmulti-dimensionalCopula’swiththe dependenceofMarkovtreestructures. Butbecausethesizeofthevariablesincreases the structure of these graphical models are complex and time-consuming. Therefore, we can consider the conditions of models in a fully Bayesian framework contract. So that the tree and other tree-dependent parameters can be defined by the prior,and then get their posterior distributions. Because tree structures are related to each other variables, in this thesis using Markov Chain Monte Carlo simulation methods to compare the proposals of tree structures is investigated.

در اين پايان ­نامه، كاربرد مدل­ هايبيز ناپارامتري در وظايف پردازش زبان طبيعي مورد مطالعه قرار داده شده­ اند. ابتدا روش ­هايبيز ناپارامتري براساس رايج ­ترين توزيع پيشين يعني فرايند ديريكله مورد مطالعهقرار گرفته­ اند. سپس نمايش­ هاي متفاوت از فرايند ديريكله مانند طرح كيسه پوليا،فرايند رستوران چيني و ساختار استيك بريكينگ معرفي شده ­اند. در ادامه به معرفي دو فرايند توليد شده توسط فرايند­هاي ديريكلهيعني فرايند­هايديريكله­ سلسله مراتبي و فرايند­هاي پيتمن يور پرداخته شده است. در پايان 4 راه­ حلپيشنهادي بيز ناپارامتري در وظايف پردازش زبان طبيعي از جمله تقسيم­ بندي كلمه،استخراج عبارت و صف­ بندي، تجزيه­ مستقل از متن و مدل­سازي زبان ارائه شده ­اند.

  Regression is used to predict and express variations of a variable based on other variables. In fact, statistical regression analysis and statistical techniques are used to examine and model the relationship between variables. Linear regression is one of the most widely used statistical tools. Modern regression applications for large data sets have created new challenges. when the number of variables approaches or exceeds the number of samples, We will consider a new method in this thesis that applies to many genomic databases. This method is called the Ising Bayesian Approximation (BIA). This method is used to quickly calculate the latent probabilities for the fit of the characteristic in the linear regression L2 compensated. From a practical point of view, BIA provides an algorithm for computing effective Bayesian paths for regression compensated L2. Using this method, it is possible to calcugate the latent likelihood of fit for a collection of dataset data, as is commonly found in genomic studies. The importance of this study is to consider the relationship between the features when evaluating meaningful statistics in the large data set. When the number of properties is high, even low correlations can lead to a decrease in the characteristics of the later probabilities. In this thesis, We also show that choosing a probability threshold for examining the importance of high-demention issues is usually not logical. Instead, BIA can be used as part of a two-step process in which BIA is used to quickly eliminate inappropriate variables, that is, variables that have a lower rating in the later probability before a rigorous validation process, from the computational point for the deduction of coefficients regression to be used the computational influence of BIA and the existence of a natural threshold for the penalized parameter are used, the two-step process is appropriate

برآورد تابع بقا و عوامل موثر بر بيماران مبتلا به سرطان پستان در عراق از سال 2014 تا 2016  

 for analyises emax model can that baysian D-optimal desition for E-max model

Recently, one of the subjects that is attractive for statisticians on applied fields, is optimal designs to do the experiments. Optimal designs are obtaind using real-valued function which is call optimal criteria.Statistical models to study the behavior of absorption or Drog release are called statistical models in pharmacokinetic/pharmacodynamics. In this thesis, we consider optimal designs for models in pharmacokinetic/pharmacodynamics studies.Since that information matrixs for these models depend on the unknown parameters, locally optimal designs have been considered to find optimal designs. Numerical results have been obtained for D-, A-, E-optimal designs.

Determination of optimal design for testing procedures is one of the major topics of interest to most statisticians. These designs are commonly obtained by optimizing some functions of information matrix to acquire the most appropriate parameter estimates. But many results on optimal designs of experiments are derived under the assumption that the statistical model is known at the design stage. Thus, the purpose of an experiment should be dual: to determine which of more rival models is the more adequate and then to estimate the parameters of the chosen model. In the present thesis, study DKL and DT optimality

Optimal ‎designs ‎as a‎ ‎tool, ‎which ‎help ‎researchers ‎to ‎predict ‎more ‎accurate ‎results, ‎has ‎been ‎commonly ‎considered ‎for ‎along ‎time. ‎Most ‎of ‎these ‎researches ‎are ‎based ‎on ‎the ‎Linear ‎models ‎with ‎normal ‎distribution ‎for ‎response ‎variable. ‎Another ‎assumption ‎which ‎has ‎been ‎considered ‎in ‎the ‎regular literatures, ‎is ‎the ‎independency ‎on ‎predictor ‎variables. ‎In ‎the ‎present ‎thesis, ‎we ‎study ‎Poisson ‎regression ‎model ‎as a‎ ‎special ‎case ‎of ‎generalized ‎linear ‎models. ‎Also ‎we ‎consider ‎some ‎cases ‎with ‎dependent‎ ‎predictor ‎variables. ‎‏‎$‎‎‎A-‎$‎optimal ‎designs ‎obtain ‎for ‎Poisson ‎regression ‎model ‎and ‎Poisson ‎ridge ‎regression ‎model. ‎We ‎also ‎calculate ‎ridge ‎parameter ‎based ‎on a‎ ‎new ‎method. ‎The ‎new ‎method ‎to ‎find ‎the ‎new ‎ridge ‎parameter, ‎compare ‎to ‎the ‎some ‎previous ‎methods.

  Using optimum experimental design to run an experiment is one of the topics in applied statistics which isconsidered by some statisticians. Design of a experiment for statistical regression models is very important.In this thesis and making optimal plans for generalized linear regression model Gompertz model in thefamily has been placed. In order to find optimal designs of optimality criteria shall be used. These criteriaare usually functions of the matrix. Given that in generalized linear models, matrix depends on unknownparameters of the model, so in this thesis using D -Bhyngy Bayesian Criterion, schemeD parser Bayesianregression model Gompertz is calculated.

  Optimal designs play an important role in marketing research, medical and the other sciences.Using of these designs can be reduced the cost of researche and experiments. To calculate theoptimal design need to have an optimality criterion. In this thesis, D-optimal criterion hasbeen considered which is a function of the Fisher information matrix. In the nonlinear models,the Fisher information matrix depends on unknown parameters will cause inconsistenciesin the design. There are some techniques to solve this problem of dependence optimalitycriterion on unknown parameters. In this situation, it can be pointed to three of themas follows: 1- The localy optimal design, 2- Minimax optimal design, 3- Bayesian optimaldesign. In this thesis, Inverse Quadratic Polynomial regression model will be introduced.Then, Bayesian D-optimal design for this model on the based on prior distribution uniformand normal for unknown parameters will be obtained.

 Comparing risks play an important role in insurance statistics. One of the ways to compare risks is by using the measures of risk. In actuarial literature, considering tail variabilities of risks which are   low frequency and   high severity losses is vital. While in many cases, comparing based on different risk measures will be followed various results as well as using a risk measure in different cases. Furthermore, we cannot also propose an explicit expressions for risk measure under a special statistical distribution.   Because of these limitations, actuaries should use stochastic orders for ordering risks. Therefore, comparison of random risks with using the   functions of probability   distributions as Tail ,   top Loss,   excess-Mean functions and etc is more helpful than comparing based on some   umerical criteria associated distributions. The comparison of the Random risks with using mentioned functions which usually produce partial orders among probability distributions is called “Stochastic Orders.”In this thesis, firstly, The risk concept, some measures of risk and type of stochastic orders are introduced which allow us to compare variabilites between random variables. Then, the relationships between the excess wealth order and other familiar stochastic variability orders (Dispersive Order, Stop Loss, convex, star and mean-excess) has been studied. In the reminder of this thesis, some characterizations of variability stochastic orders are showed by using the usual and distortion risk measures.

  In the recent years, many researches on dynamic measures of uncertainty have been carriedout which indicate their practical importance. One of the related interesting issues is thenonparametric estimation of such measures. Since in the reliability and survival analysis,samples usually contain censored data, so in this thesis, using the kernel density estimation,we investigate the nonparametric estimation of generalized past entropy and Renyi’s residualentropy based on the censored data. Some of the asymptotic properties of the estimators arestudied.